1. Field of the Invention
The invention relates to an interior permanent magnet machine having a rotor with multiple laminations in axially stacked relationship.
2. Background Discussion
An interior permanent magnet machine typically includes a stator with a ferrous metal core comprising stacked laminations, stator coil windings that carry excitation current and a rotor with circumferentially spaced permanent magnets on the rotor periphery that cooperate with circumferentially spaced stator poles. The stator poles are separated from the periphery of the rotor by a calibrated air gap. When the machine is acting as a motor, the coils are energized by an electrical current to provide rotor torque. The current has an alternating, multiple-phase waveform of sinusoidal shape. The interaction of an electromagnetic flux flow path created by the stator windings with the flux flow path created by the permanent magnets typically is accompanied by harmonic waveform components that induce motor torque fluctuations. Harmonic flux waveform components are created because the stator has windings contained in slots rather than in a uniform sinusoidal distribution along the inner circumference of the stator. The rotor flux also has harmonic flux because of discrete permanent magnet shapes and sizes. These features are manifested by a motor torque ripple, or torque oscillation, accompanied by vibration and noise. Further, operating efficiency of the motor is affected adversely. High order frequencies can be filtered out by the limited bandwidth of the mechanical system of a traction drive of a hybrid electric vehicle, but low frequencies will cause unacceptable oscillations.
The biggest components of the stator and rotor fluxes are called the fundamental components. In normal operation, both the stator and rotor fundamental fluxes rotate in the same direction and at the same speed, and the interaction between the stator and rotor fundamental fluxes generate rotor torque. The stator and rotor harmonic fluxes have different pole numbers, rotation speeds and directions. As a result, the interactions between rotor and stator harmonic fluxes generate torque fluctuation, which is called torque ripple. The torque ripple has different components with different frequencies. The order of a torque ripple component is defined as the ratio of the frequency of the torque ripple component to the speed of the rotor in revolution per second.
A conventional way to reduce motor torque ripple comprises skewing axially placed sections of the rotor ripple, one section with respect to the other. The rotor typically is connected drivably to a rotor shaft using a keyway and slot driving connection. In order to offset or skew a rotor section with respect to an adjacent section, the sections are relatively rotated, usually about one-half of the stator slot pitch. If it is assumed that the rotor is divided into a given number of axial sections (k), the sections are rotated with respect to adjacent sections by an angle equal to:                Skew angle (k)=360/(k×Ns) in mechanical degrees, where Ns is the number of slots.        
The maximum rotation between any two axial sections of the rotor is:                Max relative skew angle (k)=(k−1)×360/(k×Ns) in mechanical degrees.For example, in the case of a two section, 48 slot stator, a typical value of the skew angle is 3.75°. The skewing of the rotor is intended to produce a smoother mechanical torque than would otherwise be achieved using a straight rotor. This will eliminate certain undesirable oscillations or ripple of the torque caused by harmonics present in the air gap flux and in the air gap permeance.        
For permanent magnet machines it is also common practice to skew the permanent magnets rather than the sections. However, the skewing method cannot eliminate all the torque ripple components because it cannot be designed to be effective to reduce all the torque ripple components. Another disadvantage of the skewing technique is that the average torque is also reduced, resulting in a de-rating with respect to the non-skewed design. Also, from a manufacturing perspective, skewing of either stator or rotor cores results in added complexity and cost.